I have a project with multiple video files that I want to pack for a render farm how should I do this?
Blender doesn't pack videos nor image sequences. If you want that to be possible in the future, you can upvote this rightclickselect proposal I made. But know that it has little chance to happen.

However, Sheep it supports .zip files and linked datablocks. So I'm pretty confident videos should work this way.
Zacharias Reinhardt explains how to use linked assets with Sheep it in this tutorial (link goes to the appropriate timecode).